Understanding the Movement of a Unique Clock

[hms.tech]

Homework Statement

see attachment

Homework Equations

θ= ω*τ

The Attempt at a Solution

Nothing. Instead I have some queries about the question itself :
1.Is this a proper clock, will it show the correct time as any normal clock ?
2.what is the angular displacement of one of the clock hand when it moves from 1 to 2.
Is this angular displacement constant every 5 minutes (ie from 1 to 2 , 2 to 3 , 3 to 4 etc ).

 

[Curious3141]

Homework Statement

see attachment
View attachment 54960

Homework Equations

θ= ω*τ

The Attempt at a Solution

Nothing. Instead I have some queries about the question itself :
1.Is this a proper clock, will it show the correct time as any normal clock ?
2.what is the angular displacement of one of the clock hand when it moves from 1 to 2.
Is this angular displacement constant every 5 minutes (ie from 1 to 2 , 2 to 3 , 3 to 4 etc ).

1. For the purposes of this question, you may assume that the *hour* will be shown exactly on the hour, ditto with the minutes in multiples of five. The interpolations between markings may not be exact, but you needn't concern yourself with this.

2. What would this be in a "regular" circular clock? Would you expect it to be different here?

3. Why wouldn't it be?

 

[hms.tech]

1. For the purposes of this question, you may assume that the *hour* will be shown exactly on the hour, ditto with the minutes in multiples of five. The interpolations between markings may not be exact, but you needn't concern yourself with this.

2. What would this be in a "regular" circular clock? Would you expect it to be different here?

3. Why wouldn't it be?

we'll consider the time in seconds for easiness.

w= ∏/30 rad per second

More help required ...

 

[NascentOxygen]

When a hand points to 12, it forms an angle with the vertical of 0°.
When a hand points to 1, it forms an angle with the vertical of ??°[/size][/color]
When a hand points to 2, it forms an angle with the vertical of ??°[/size][/color]

 

[hms.tech]

When a hand points to 12, it forms an angle with the vertical of 0°.
When a hand points to 1, it forms an angle with the vertical of ??°[/size]
When a hand points to 2, it forms an angle with the vertical of ??°[/size]

When it points to one, it forms an angle of ∏/6
When it points to two, it forms and angle with the vertical of ∏/3

 

[NascentOxygen]

So you can now on the clock face draw some triangles showing lengths and angles, for a hand pointing to 1, and also for it pointing to 2.

 

[hms.tech]

So you can now on the clock face draw some triangles showing lengths and angles, for a hand pointing to 1, and also for it pointing to 2.

Aren't these angles only applicable to a normal "round clock" ?

 

[NascentOxygen]

Each hand moves at a constant angular rotation, like an ordinary clock, we are told.

 

[LCKurtz]

Aren't these angles only applicable to a normal "round clock" ?

Draw a round clock in the same picture centered between 6 and 12 and extend the radii.

 

[Curious3141]

Aren't these angles only applicable to a normal "round clock" ?

These angles are applicable to this clock, because you're told the hands move like a normal (round) clock.

You might find it easier to visualise the problem if you express everything in degrees. Consider the hand at position "n" and then at position "n+2" (two markings apart). What's the angle between those two positions?

Do you see a special triangle here? This makes things quite easy, along with some very simple trig.

You could take up LCKurtz's suggestion to draw a round clock, but personally, I think it might complicate things if you clutter the figure with a circle. I would suggest just drawing the rectangle and the various triangles within it and treating the problem as simple geometry and trig.